Electrostatic potential and field near the boundary between space charge and no charge regions within a cylindrical pipe

In electronic industries, a corona ionizer is widely used for the elimination of electrostatic charge on the material. Although the high frequency AC ionizer proved the effectiveness of its performance, the corona ions must be sent through a metal pipe to reach targeting area. In order to analyze the behavior of ions in elimination process, the potential and electric field within a pipe must be known. Since the potential and field distribution near the boundary between space charge and no charge regions are extremely important, the analytical solution for this problem was sought by using Bessel functions. Analytical solution showed that even in no charge region, there exists potential distribution within a pipe. Numerical calculation of electric field on the inner pipe surface indicated useful information to estimate the charge density in the pipe. Furthermore, some mathematical formulae were obtained by using Bessel functions.